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  <h3><a href="../contents.html">Table of Contents</a></h3>
  <ul>
<li><a class="reference internal" href="#">Chebyshev Module (<code class="xref py py-mod docutils literal notranslate"><span class="pre">numpy.polynomial.chebyshev</span></code>)</a><ul>
<li><a class="reference internal" href="#chebyshev-class">Chebyshev Class</a></li>
<li><a class="reference internal" href="#basics">Basics</a></li>
<li><a class="reference internal" href="#fitting">Fitting</a></li>
<li><a class="reference internal" href="#calculus">Calculus</a></li>
<li><a class="reference internal" href="#algebra">Algebra</a></li>
<li><a class="reference internal" href="#quadrature">Quadrature</a></li>
<li><a class="reference internal" href="#miscellaneous">Miscellaneous</a></li>
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  <div class="section" id="chebyshev-module-numpy-polynomial-chebyshev">
<h1>Chebyshev Module (<code class="xref py py-mod docutils literal notranslate"><span class="pre">numpy.polynomial.chebyshev</span></code>)<a class="headerlink" href="#chebyshev-module-numpy-polynomial-chebyshev" title="Permalink to this headline">¶</a></h1>
<div class="versionadded">
<p><span class="versionmodified added">New in version 1.4.0.</span></p>
</div>
<p>This module provides a number of objects (mostly functions) useful for
dealing with Chebyshev series, including a <a class="reference internal" href="generated/numpy.polynomial.chebyshev.Chebyshev.html#numpy.polynomial.chebyshev.Chebyshev" title="numpy.polynomial.chebyshev.Chebyshev"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Chebyshev</span></code></a> class that
encapsulates the usual arithmetic operations.  (General information
on how this module represents and works with such polynomials is in the
docstring for its “parent” sub-package, <a class="reference internal" href="routines.polynomials.package.html#module-numpy.polynomial" title="numpy.polynomial"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.polynomial</span></code></a>).</p>
<div class="section" id="chebyshev-class">
<h2>Chebyshev Class<a class="headerlink" href="#chebyshev-class" title="Permalink to this headline">¶</a></h2>
<table class="longtable docutils align-default">
<colgroup>
<col style="width: 10%" />
<col style="width: 90%" />
</colgroup>
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/numpy.polynomial.chebyshev.Chebyshev.html#numpy.polynomial.chebyshev.Chebyshev" title="numpy.polynomial.chebyshev.Chebyshev"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Chebyshev</span></code></a>(coef[, domain, window])</p></td>
<td><p>A Chebyshev series class.</p></td>
</tr>
</tbody>
</table>
</div>
<div class="section" id="basics">
<h2>Basics<a class="headerlink" href="#basics" title="Permalink to this headline">¶</a></h2>
<table class="longtable docutils align-default">
<colgroup>
<col style="width: 10%" />
<col style="width: 90%" />
</colgroup>
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/numpy.polynomial.chebyshev.chebval.html#numpy.polynomial.chebyshev.chebval" title="numpy.polynomial.chebyshev.chebval"><code class="xref py py-obj docutils literal notranslate"><span class="pre">chebval</span></code></a>(x, c[, tensor])</p></td>
<td><p>Evaluate a Chebyshev series at points x.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/numpy.polynomial.chebyshev.chebval2d.html#numpy.polynomial.chebyshev.chebval2d" title="numpy.polynomial.chebyshev.chebval2d"><code class="xref py py-obj docutils literal notranslate"><span class="pre">chebval2d</span></code></a>(x, y, c)</p></td>
<td><p>Evaluate a 2-D Chebyshev series at points (x, y).</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/numpy.polynomial.chebyshev.chebval3d.html#numpy.polynomial.chebyshev.chebval3d" title="numpy.polynomial.chebyshev.chebval3d"><code class="xref py py-obj docutils literal notranslate"><span class="pre">chebval3d</span></code></a>(x, y, z, c)</p></td>
<td><p>Evaluate a 3-D Chebyshev series at points (x, y, z).</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/numpy.polynomial.chebyshev.chebgrid2d.html#numpy.polynomial.chebyshev.chebgrid2d" title="numpy.polynomial.chebyshev.chebgrid2d"><code class="xref py py-obj docutils literal notranslate"><span class="pre">chebgrid2d</span></code></a>(x, y, c)</p></td>
<td><p>Evaluate a 2-D Chebyshev series on the Cartesian product of x and y.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/numpy.polynomial.chebyshev.chebgrid3d.html#numpy.polynomial.chebyshev.chebgrid3d" title="numpy.polynomial.chebyshev.chebgrid3d"><code class="xref py py-obj docutils literal notranslate"><span class="pre">chebgrid3d</span></code></a>(x, y, z, c)</p></td>
<td><p>Evaluate a 3-D Chebyshev series on the Cartesian product of x, y, and z.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/numpy.polynomial.chebyshev.chebroots.html#numpy.polynomial.chebyshev.chebroots" title="numpy.polynomial.chebyshev.chebroots"><code class="xref py py-obj docutils literal notranslate"><span class="pre">chebroots</span></code></a>(c)</p></td>
<td><p>Compute the roots of a Chebyshev series.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/numpy.polynomial.chebyshev.chebfromroots.html#numpy.polynomial.chebyshev.chebfromroots" title="numpy.polynomial.chebyshev.chebfromroots"><code class="xref py py-obj docutils literal notranslate"><span class="pre">chebfromroots</span></code></a>(roots)</p></td>
<td><p>Generate a Chebyshev series with given roots.</p></td>
</tr>
</tbody>
</table>
</div>
<div class="section" id="fitting">
<h2>Fitting<a class="headerlink" href="#fitting" title="Permalink to this headline">¶</a></h2>
<table class="longtable docutils align-default">
<colgroup>
<col style="width: 10%" />
<col style="width: 90%" />
</colgroup>
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/numpy.polynomial.chebyshev.chebfit.html#numpy.polynomial.chebyshev.chebfit" title="numpy.polynomial.chebyshev.chebfit"><code class="xref py py-obj docutils literal notranslate"><span class="pre">chebfit</span></code></a>(x, y, deg[, rcond, full, w])</p></td>
<td><p>Least squares fit of Chebyshev series to data.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/numpy.polynomial.chebyshev.chebvander.html#numpy.polynomial.chebyshev.chebvander" title="numpy.polynomial.chebyshev.chebvander"><code class="xref py py-obj docutils literal notranslate"><span class="pre">chebvander</span></code></a>(x, deg)</p></td>
<td><p>Pseudo-Vandermonde matrix of given degree.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/numpy.polynomial.chebyshev.chebvander2d.html#numpy.polynomial.chebyshev.chebvander2d" title="numpy.polynomial.chebyshev.chebvander2d"><code class="xref py py-obj docutils literal notranslate"><span class="pre">chebvander2d</span></code></a>(x, y, deg)</p></td>
<td><p>Pseudo-Vandermonde matrix of given degrees.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/numpy.polynomial.chebyshev.chebvander3d.html#numpy.polynomial.chebyshev.chebvander3d" title="numpy.polynomial.chebyshev.chebvander3d"><code class="xref py py-obj docutils literal notranslate"><span class="pre">chebvander3d</span></code></a>(x, y, z, deg)</p></td>
<td><p>Pseudo-Vandermonde matrix of given degrees.</p></td>
</tr>
</tbody>
</table>
</div>
<div class="section" id="calculus">
<h2>Calculus<a class="headerlink" href="#calculus" title="Permalink to this headline">¶</a></h2>
<table class="longtable docutils align-default">
<colgroup>
<col style="width: 10%" />
<col style="width: 90%" />
</colgroup>
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/numpy.polynomial.chebyshev.chebder.html#numpy.polynomial.chebyshev.chebder" title="numpy.polynomial.chebyshev.chebder"><code class="xref py py-obj docutils literal notranslate"><span class="pre">chebder</span></code></a>(c[, m, scl, axis])</p></td>
<td><p>Differentiate a Chebyshev series.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/numpy.polynomial.chebyshev.chebint.html#numpy.polynomial.chebyshev.chebint" title="numpy.polynomial.chebyshev.chebint"><code class="xref py py-obj docutils literal notranslate"><span class="pre">chebint</span></code></a>(c[, m, k, lbnd, scl, axis])</p></td>
<td><p>Integrate a Chebyshev series.</p></td>
</tr>
</tbody>
</table>
</div>
<div class="section" id="algebra">
<h2>Algebra<a class="headerlink" href="#algebra" title="Permalink to this headline">¶</a></h2>
<table class="longtable docutils align-default">
<colgroup>
<col style="width: 10%" />
<col style="width: 90%" />
</colgroup>
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<tr class="row-odd"><td><p><a class="reference internal" href="generated/numpy.polynomial.chebyshev.chebadd.html#numpy.polynomial.chebyshev.chebadd" title="numpy.polynomial.chebyshev.chebadd"><code class="xref py py-obj docutils literal notranslate"><span class="pre">chebadd</span></code></a>(c1, c2)</p></td>
<td><p>Add one Chebyshev series to another.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/numpy.polynomial.chebyshev.chebsub.html#numpy.polynomial.chebyshev.chebsub" title="numpy.polynomial.chebyshev.chebsub"><code class="xref py py-obj docutils literal notranslate"><span class="pre">chebsub</span></code></a>(c1, c2)</p></td>
<td><p>Subtract one Chebyshev series from another.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/numpy.polynomial.chebyshev.chebmul.html#numpy.polynomial.chebyshev.chebmul" title="numpy.polynomial.chebyshev.chebmul"><code class="xref py py-obj docutils literal notranslate"><span class="pre">chebmul</span></code></a>(c1, c2)</p></td>
<td><p>Multiply one Chebyshev series by another.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/numpy.polynomial.chebyshev.chebmulx.html#numpy.polynomial.chebyshev.chebmulx" title="numpy.polynomial.chebyshev.chebmulx"><code class="xref py py-obj docutils literal notranslate"><span class="pre">chebmulx</span></code></a>(c)</p></td>
<td><p>Multiply a Chebyshev series by x.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/numpy.polynomial.chebyshev.chebdiv.html#numpy.polynomial.chebyshev.chebdiv" title="numpy.polynomial.chebyshev.chebdiv"><code class="xref py py-obj docutils literal notranslate"><span class="pre">chebdiv</span></code></a>(c1, c2)</p></td>
<td><p>Divide one Chebyshev series by another.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/numpy.polynomial.chebyshev.chebpow.html#numpy.polynomial.chebyshev.chebpow" title="numpy.polynomial.chebyshev.chebpow"><code class="xref py py-obj docutils literal notranslate"><span class="pre">chebpow</span></code></a>(c, pow[, maxpower])</p></td>
<td><p>Raise a Chebyshev series to a power.</p></td>
</tr>
</tbody>
</table>
</div>
<div class="section" id="quadrature">
<h2>Quadrature<a class="headerlink" href="#quadrature" title="Permalink to this headline">¶</a></h2>
<table class="longtable docutils align-default">
<colgroup>
<col style="width: 10%" />
<col style="width: 90%" />
</colgroup>
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/numpy.polynomial.chebyshev.chebgauss.html#numpy.polynomial.chebyshev.chebgauss" title="numpy.polynomial.chebyshev.chebgauss"><code class="xref py py-obj docutils literal notranslate"><span class="pre">chebgauss</span></code></a>(deg)</p></td>
<td><p>Gauss-Chebyshev quadrature.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/numpy.polynomial.chebyshev.chebweight.html#numpy.polynomial.chebyshev.chebweight" title="numpy.polynomial.chebyshev.chebweight"><code class="xref py py-obj docutils literal notranslate"><span class="pre">chebweight</span></code></a>(x)</p></td>
<td><p>The weight function of the Chebyshev polynomials.</p></td>
</tr>
</tbody>
</table>
</div>
<div class="section" id="miscellaneous">
<h2>Miscellaneous<a class="headerlink" href="#miscellaneous" title="Permalink to this headline">¶</a></h2>
<table class="longtable docutils align-default">
<colgroup>
<col style="width: 10%" />
<col style="width: 90%" />
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<tr class="row-odd"><td><p><a class="reference internal" href="generated/numpy.polynomial.chebyshev.chebcompanion.html#numpy.polynomial.chebyshev.chebcompanion" title="numpy.polynomial.chebyshev.chebcompanion"><code class="xref py py-obj docutils literal notranslate"><span class="pre">chebcompanion</span></code></a>(c)</p></td>
<td><p>Return the scaled companion matrix of c.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/numpy.polynomial.chebyshev.chebdomain.html#numpy.polynomial.chebyshev.chebdomain" title="numpy.polynomial.chebyshev.chebdomain"><code class="xref py py-obj docutils literal notranslate"><span class="pre">chebdomain</span></code></a></p></td>
<td><p></p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/numpy.polynomial.chebyshev.chebzero.html#numpy.polynomial.chebyshev.chebzero" title="numpy.polynomial.chebyshev.chebzero"><code class="xref py py-obj docutils literal notranslate"><span class="pre">chebzero</span></code></a></p></td>
<td><p></p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/numpy.polynomial.chebyshev.chebone.html#numpy.polynomial.chebyshev.chebone" title="numpy.polynomial.chebyshev.chebone"><code class="xref py py-obj docutils literal notranslate"><span class="pre">chebone</span></code></a></p></td>
<td><p></p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/numpy.polynomial.chebyshev.chebx.html#numpy.polynomial.chebyshev.chebx" title="numpy.polynomial.chebyshev.chebx"><code class="xref py py-obj docutils literal notranslate"><span class="pre">chebx</span></code></a></p></td>
<td><p></p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/numpy.polynomial.chebyshev.chebtrim.html#numpy.polynomial.chebyshev.chebtrim" title="numpy.polynomial.chebyshev.chebtrim"><code class="xref py py-obj docutils literal notranslate"><span class="pre">chebtrim</span></code></a>(c[, tol])</p></td>
<td><p>Remove “small” “trailing” coefficients from a polynomial.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/numpy.polynomial.chebyshev.chebline.html#numpy.polynomial.chebyshev.chebline" title="numpy.polynomial.chebyshev.chebline"><code class="xref py py-obj docutils literal notranslate"><span class="pre">chebline</span></code></a>(off, scl)</p></td>
<td><p>Chebyshev series whose graph is a straight line.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/numpy.polynomial.chebyshev.cheb2poly.html#numpy.polynomial.chebyshev.cheb2poly" title="numpy.polynomial.chebyshev.cheb2poly"><code class="xref py py-obj docutils literal notranslate"><span class="pre">cheb2poly</span></code></a>(c)</p></td>
<td><p>Convert a Chebyshev series to a polynomial.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/numpy.polynomial.chebyshev.poly2cheb.html#numpy.polynomial.chebyshev.poly2cheb" title="numpy.polynomial.chebyshev.poly2cheb"><code class="xref py py-obj docutils literal notranslate"><span class="pre">poly2cheb</span></code></a>(pol)</p></td>
<td><p>Convert a polynomial to a Chebyshev series.</p></td>
</tr>
</tbody>
</table>
</div>
</div>


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